Eli5 How it is decided whose clock is running slower, given motion is always relative?
In: 4
Well, the very short answer is two things. First, the answer in a static system (everything stays at the same velocity relative to each other) is that they both do, depending upon who is measuring. The second is that, for cases where we can bring the clocks together again, we can do the measurements ourselves. We can actually measure which one is slower if we use really sensitive ways of measuring time (atomic clocks) and/or very fast objects (particles in particle accelerators).
However, this doesn’t explain why, if motion is relative, one of them is actually slower. This is because, in Special Relativity, it is true that neither of them is and the motion between them is relative, but it is too limited to cover most of the real world. That is why Einstein had to devise General Relativity.
Special Relativity works only if the two clocks are traveling at a constant velocity relative to each other without interference by gravity. Under these conditions, which clock is actually slower is a matter of who you ask. Each clock appears to be the faster to those traveling with it, and an outside observer will get different answers depending upon their velocity relative to the clocks.
However, it doesn’t work if the two objects change velocity relative to one another.
Suppose I have two clocks on spaceships passing each other at speeds approaching the speed of light. Each spaceship’s clock shows the other one as running slower. Suppose that this rate is such that each ship sees the other ship as having a clock running at half speed. This is Special Relativity.
But what happens if one spaceship changes its course and chases after the other spaceship until they eventually meet up at zero velocity relative to each other and in the same location?
Suppose they pass each other, and they each see the other as having a slower clock. They pass, each seeing themselves as standing still and the other as racing by. Both declare the point in time that they pass as “mark”.
One spaceship is so fast that, according to its own clock, it is able to chase down the other ship in two hours. So, it does.
So, what happens?
Well, Einstein reasoned that the clocks couldn’t both be behind when the two ships met. One of them had to show less time since mark than the other, i.e. it was “behind”. This meant that one of them had to go through a period of time when it was so much slower than the other that when they met up it would be behind by the proper amount.
So which one?
Well, motion is relative up to a point. If I am moving at a constant velocity in a straight line with no outside forces such as gravity acting upon me, then I can treat myself as stationary. If I cannot see outside my spaceship, then for my purposes, I ***am*** stationary.
But this doesn’t apply to the spaceship that caught up with the other one. Even if I cannot see outside I feel acceleration. I am not motionless even by my own measurements. I am not stationary.
This meant that the difference between the two was acceleration. Acceleration altered the measurement of time. I might not be able to see my clock slow down, but there was a factor that told me that I was not moving at a constant speed. My frame of reference changed, and to make things match up when the two frames of reference met up, the frame of reference that was subject to acceleration turned out to be the slow one.
Further reasoning showed that from the point of view of an observer inside one of the ships who couldn’t see out, acceleration and gravity were identical. This meant that gravity, too, should slow time in exactly the same way that acceleration did. In a very real sense, they were the same thing.
This is the theoretical basis. When we tried this in the real world, we found that it was true. Measurements have repeatedly shown that the predictions of General Relativity are true, to the point that GPS wouldn’t work properly without taking them into account.
So, Einstein told us which clock would be slower and gave us the math to figure out which one, and every test we have made since says that he was right.
Latest Answers